theorem Th59:
  i in Class(equivalence_wrt FI,k) & j in Class(equivalence_wrt FI
  ,k) implies i"\/"j in Class(equivalence_wrt FI,k) & i"/\" j in Class(
  equivalence_wrt FI,k)
proof
  assume that
A1: i in Class(equivalence_wrt FI,k) and
A2: j in Class(equivalence_wrt FI,k);
A3: i <=> k in FI by A1,Lm4;
A4: j <=> k in FI by A2,Lm4;
  k"/\"k = k;
  then
A5: (i"/\"j) <=> k in FI by A3,A4,Th58;
  k"\/"k = k;
  then (i"\/"j) <=> k in FI by A3,A4,Th58;
  hence thesis by A5,Lm4;
end;
